<!DOCTYPE html>
<html lang="zh-CN">
<head>
  <meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=2">
<meta name="theme-color" content="#222">
<meta name="generator" content="Hexo 5.4.2">
  <link rel="apple-touch-icon" sizes="180x180" href="/images/apple-touch-icon-next.png">
  <link rel="icon" type="image/png" sizes="32x32" href="/images/favicon-32x32-next.png">
  <link rel="icon" type="image/png" sizes="16x16" href="/images/favicon-16x16-next.png">
  <link rel="mask-icon" href="/images/logo.svg" color="#222">

<link rel="stylesheet" href="/css/main.css">


<link rel="stylesheet" href="/lib/font-awesome/css/all.min.css">

<script id="hexo-configurations">
    var NexT = window.NexT || {};
    var CONFIG = {"hostname":"wrr123.github.io","root":"/","scheme":"Muse","version":"7.8.0","exturl":false,"sidebar":{"position":"left","display":"post","padding":18,"offset":12,"onmobile":false},"copycode":{"enable":false,"show_result":false,"style":null},"back2top":{"enable":true,"sidebar":false,"scrollpercent":false},"bookmark":{"enable":false,"color":"#222","save":"auto"},"fancybox":false,"mediumzoom":false,"lazyload":false,"pangu":false,"comments":{"style":"tabs","active":null,"storage":true,"lazyload":false,"nav":null},"algolia":{"hits":{"per_page":10},"labels":{"input_placeholder":"Search for Posts","hits_empty":"We didn't find any results for the search: ${query}","hits_stats":"${hits} results found in ${time} ms"}},"localsearch":{"enable":true,"trigger":"auto","top_n_per_article":1,"unescape":false,"preload":false},"motion":{"enable":true,"async":false,"transition":{"post_block":"fadeIn","post_header":"slideDownIn","post_body":"slideDownIn","coll_header":"slideLeftIn","sidebar":"slideUpIn"}},"path":"search.json"};
  </script>

  <meta name="description" content="基本概念递归算法是一种直接或间接调用自身函数或方法的算法。 Java 递归算法是基于 Java 语言实现的递归算法。 递归算法的实质是把问题分解成规模缩小的同类问题的子问题，然后递归调用方法来表示问题的解。 递归算法对解决一大类问题很有效，它可以使算法简洁和易于理解。  递归算法，其实说白了，就是程序的自身调用。它表现在一段程序中往往会遇到调用自身的那样一种coding策略，这样我们就可以利用大道">
<meta property="og:type" content="article">
<meta property="og:title" content="递归算法">
<meta property="og:url" content="https://wrr123.github.io/2020/08/17/%E9%80%92%E5%BD%92%E7%AE%97%E6%B3%95/index.html">
<meta property="og:site_name" content="一缕烟气">
<meta property="og:description" content="基本概念递归算法是一种直接或间接调用自身函数或方法的算法。 Java 递归算法是基于 Java 语言实现的递归算法。 递归算法的实质是把问题分解成规模缩小的同类问题的子问题，然后递归调用方法来表示问题的解。 递归算法对解决一大类问题很有效，它可以使算法简洁和易于理解。  递归算法，其实说白了，就是程序的自身调用。它表现在一段程序中往往会遇到调用自身的那样一种coding策略，这样我们就可以利用大道">
<meta property="og:locale" content="zh_CN">
<meta property="article:published_time" content="2020-08-17T05:31:18.000Z">
<meta property="article:modified_time" content="2022-02-18T02:52:04.558Z">
<meta property="article:author" content="田园隐士">
<meta property="article:tag" content="java">
<meta property="article:tag" content="算法">
<meta name="twitter:card" content="summary">

<link rel="canonical" href="https://wrr123.github.io/2020/08/17/%E9%80%92%E5%BD%92%E7%AE%97%E6%B3%95/">


<script id="page-configurations">
  // https://hexo.io/docs/variables.html
  CONFIG.page = {
    sidebar: "",
    isHome : false,
    isPost : true,
    lang   : 'zh-CN'
  };
</script>

  <title>递归算法 | 一缕烟气</title>
  






  <noscript>
  <style>
  .use-motion .brand,
  .use-motion .menu-item,
  .sidebar-inner,
  .use-motion .post-block,
  .use-motion .pagination,
  .use-motion .comments,
  .use-motion .post-header,
  .use-motion .post-body,
  .use-motion .collection-header { opacity: initial; }

  .use-motion .site-title,
  .use-motion .site-subtitle {
    opacity: initial;
    top: initial;
  }

  .use-motion .logo-line-before i { left: initial; }
  .use-motion .logo-line-after i { right: initial; }
  </style>
</noscript>

<link rel="alternate" href="/atom.xml" title="一缕烟气" type="application/atom+xml">
</head>

<body itemscope itemtype="http://schema.org/WebPage">
  <div class="container use-motion">
    <div class="headband"></div>

    <header class="header" itemscope itemtype="http://schema.org/WPHeader">
      <div class="header-inner"><div class="site-brand-container">
  <div class="site-nav-toggle">
    <div class="toggle" aria-label="切换导航栏">
      <span class="toggle-line toggle-line-first"></span>
      <span class="toggle-line toggle-line-middle"></span>
      <span class="toggle-line toggle-line-last"></span>
    </div>
  </div>

  <div class="site-meta">

    <a href="/" class="brand" rel="start">
      <span class="logo-line-before"><i></i></span>
      <h1 class="site-title">一缕烟气</h1>
      <span class="logo-line-after"><i></i></span>
    </a>
      <p class="site-subtitle" itemprop="description">沧海月明珠有泪，蓝田日暖玉生烟</p>
  </div>

  <div class="site-nav-right">
    <div class="toggle popup-trigger">
        <i class="fa fa-search fa-fw fa-lg"></i>
    </div>
  </div>
</div>




<nav class="site-nav">
  <ul id="menu" class="main-menu menu">
        <li class="menu-item menu-item-home">

    <a href="/" rel="section"><i class="fa fa-home fa-fw"></i>首页</a>

  </li>
        <li class="menu-item menu-item-archives">

    <a href="/archives/" rel="section"><i class="fa fa-archive fa-fw"></i>归档</a>

  </li>
      <li class="menu-item menu-item-search">
        <a role="button" class="popup-trigger"><i class="fa fa-search fa-fw"></i>搜索
        </a>
      </li>
  </ul>
</nav>



  <div class="search-pop-overlay">
    <div class="popup search-popup">
        <div class="search-header">
  <span class="search-icon">
    <i class="fa fa-search"></i>
  </span>
  <div class="search-input-container">
    <input autocomplete="off" autocapitalize="off"
           placeholder="搜索..." spellcheck="false"
           type="search" class="search-input">
  </div>
  <span class="popup-btn-close">
    <i class="fa fa-times-circle"></i>
  </span>
</div>
<div id="search-result">
  <div id="no-result">
    <i class="fa fa-spinner fa-pulse fa-5x fa-fw"></i>
  </div>
</div>

    </div>
  </div>

</div>
    </header>

    
  <div class="back-to-top">
    <i class="fa fa-arrow-up"></i>
    <span>0%</span>
  </div>


    <main class="main">
      <div class="main-inner">
        <div class="content-wrap">
          

          <div class="content post posts-expand">
            

    
  
  
  <article itemscope itemtype="http://schema.org/Article" class="post-block" lang="zh-CN">
    <link itemprop="mainEntityOfPage" href="https://wrr123.github.io/2020/08/17/%E9%80%92%E5%BD%92%E7%AE%97%E6%B3%95/">

    <span hidden itemprop="author" itemscope itemtype="http://schema.org/Person">
      <meta itemprop="image" content="/images/avatar.gif">
      <meta itemprop="name" content="田园隐士">
      <meta itemprop="description" content="talk is cheap, show me the code">
    </span>

    <span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization">
      <meta itemprop="name" content="一缕烟气">
    </span>
      <header class="post-header">
        <h1 class="post-title" itemprop="name headline">
          递归算法
        </h1>

        <div class="post-meta">
            <span class="post-meta-item">
              <span class="post-meta-item-icon">
                <i class="far fa-calendar"></i>
              </span>
              <span class="post-meta-item-text">发表于</span>

              <time title="创建时间：2020-08-17 13:31:18" itemprop="dateCreated datePublished" datetime="2020-08-17T13:31:18+08:00">2020-08-17</time>
            </span>
              <span class="post-meta-item">
                <span class="post-meta-item-icon">
                  <i class="far fa-calendar-check"></i>
                </span>
                <span class="post-meta-item-text">更新于</span>
                <time title="修改时间：2022-02-18 10:52:04" itemprop="dateModified" datetime="2022-02-18T10:52:04+08:00">2022-02-18</time>
              </span>

          
            <span class="post-meta-item" title="阅读次数" id="busuanzi_container_page_pv" style="display: none;">
              <span class="post-meta-item-icon">
                <i class="fa fa-eye"></i>
              </span>
              <span class="post-meta-item-text">阅读次数：</span>
              <span id="busuanzi_value_page_pv"></span>
            </span><br>
            <span class="post-meta-item" title="本文字数">
              <span class="post-meta-item-icon">
                <i class="far fa-file-word"></i>
              </span>
                <span class="post-meta-item-text">本文字数：</span>
              <span>2.3k</span>
            </span>
            <span class="post-meta-item" title="阅读时长">
              <span class="post-meta-item-icon">
                <i class="far fa-clock"></i>
              </span>
                <span class="post-meta-item-text">阅读时长 &asymp;</span>
              <span>2 分钟</span>
            </span>

        </div>
      </header>

    
    
    
    <div class="post-body" itemprop="articleBody">

      
        <h4 id="基本概念"><a href="#基本概念" class="headerlink" title="基本概念"></a>基本概念</h4><p>递归算法是一种直接或间接调用自身函数或方法的算法。</p>
<p>Java 递归算法是基于 Java 语言实现的递归算法。</p>
<p>递归算法的实质是把问题分解成规模缩小的同类问题的子问题，然后递归调用方法来表示问题的解。</p>
<p>递归算法对解决一大类问题很有效，它可以使算法简洁和易于理解。</p>
<blockquote>
<p>递归算法，其实说白了，就是程序的自身调用。它表现在一段程序中往往会遇到调用自身的那样一种coding策略，这样我们就可以利用大道至简的思想，把一个大的复杂的问题层层转换为一个小的和原问题相似的问题来求解的这样一种策略。递归往往能给我们带来非常简洁非常直观的代码形势，从而使我们的编码大大简化，然而递归的思维确实很我们的常规思维相逆的，我们通常都是从上而下的思维问题， 而递归趋势从下往上的进行思维。这样我们就能看到我们会用很少的语句解决了非常大的问题，所以递归策略的最主要体现就是小的代码量解决了非常复杂的问题。</p>
</blockquote>
<span id="more"></span>
<h5 id="递归算法解决问题的特点："><a href="#递归算法解决问题的特点：" class="headerlink" title="递归算法解决问题的特点："></a>递归算法解决问题的特点：</h5><ol>
<li>递归就是方法里调用自身；</li>
<li>在使用递归策略时，必须有一个明确的递归结束条件，称为递归出口；</li>
<li>递归算法解题通常显得很简洁，但递归算法解题的运行效率极低。所以一般不提倡用递归算法来设计程序；</li>
<li>在递归调用的过程中系统为每一层的返回点、局部量等开辟了栈来存储。递归次数过多容易造成栈溢出等；</li>
</ol>
<p><strong>在做递归算法的时候，一定要把握住出口，也就是做递归算法必须要有一个明确的递归结束条件，这一点是非常重要的。</strong></p>
<h4 id="几个栗子"><a href="#几个栗子" class="headerlink" title="几个栗子"></a>几个栗子</h4><h5 id="①-斐波那契数列"><a href="#①-斐波那契数列" class="headerlink" title="① 斐波那契数列"></a>① 斐波那契数列</h5><p>一个栗子</p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">/**</span></span><br><span class="line"><span class="comment"> * ④ 由于斐波纳挈数列是以兔子的繁殖引入的，因此也叫“兔子数列”。它指的是这样一个数列：0,1,1,2,3,5,8,13......从这组数可以很明显看出这样一个规律：从第三个数开始，后边一个数一定是在其之前两个数的和。在数学上，斐波纳挈数列可以以这样的公式表示：F(0) = 0 F(1) = 1 F(n) = F(n-1) + F(n-2),(n&gt;=2)</span></span><br><span class="line"><span class="comment"> * <span class="doctag">@param</span> num</span></span><br><span class="line"><span class="comment"> * <span class="doctag">@return</span></span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"><span class="keyword">public</span> <span class="keyword">static</span> <span class="type">long</span> <span class="title function_">fibo</span><span class="params">(<span class="type">long</span> num)</span> &#123;</span><br><span class="line">    <span class="keyword">if</span>(num &lt;= <span class="number">1</span>) &#123;</span><br><span class="line">        <span class="keyword">return</span> num;</span><br><span class="line">    &#125;<span class="keyword">else</span> &#123;</span><br><span class="line">        <span class="keyword">return</span> fibo(num - <span class="number">1</span>) + fibo(num - <span class="number">2</span>);</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br><span class="line"></span><br></pre></td></tr></table></figure>
<h5 id="②-n-的阶乘"><a href="#②-n-的阶乘" class="headerlink" title="② n 的阶乘"></a>② n 的阶乘</h5><p><strong>0 的阶乘是 1</strong></p>
<p>一个栗子：</p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br></pre></td><td class="code"><pre><span class="line">    <span class="keyword">public</span> <span class="keyword">static</span> <span class="type">int</span> <span class="title function_">factorialOfN</span><span class="params">(<span class="type">int</span> n)</span> &#123;</span><br><span class="line">        <span class="comment">/// 递归</span></span><br><span class="line"><span class="comment">/*</span></span><br><span class="line"><span class="comment">        if(n == 0) &#123;</span></span><br><span class="line"><span class="comment">            return 1;</span></span><br><span class="line"><span class="comment">        &#125;else &#123;</span></span><br><span class="line"><span class="comment">            return n * factorialOfN(n - 1);</span></span><br><span class="line"><span class="comment">        &#125;</span></span><br><span class="line"><span class="comment">*/</span></span><br><span class="line">        <span class="comment">// 非递归</span></span><br><span class="line">        <span class="keyword">if</span>(n == <span class="number">0</span>) &#123;</span><br><span class="line">            <span class="keyword">return</span> <span class="number">1</span>;</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="type">int</span> <span class="variable">result</span> <span class="operator">=</span> <span class="number">1</span>;</span><br><span class="line">        <span class="keyword">while</span>(n &gt; <span class="number">0</span>) &#123;</span><br><span class="line">            result *= n;</span><br><span class="line">            n--;</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="keyword">return</span> result;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br></pre></td></tr></table></figure>
<h5 id="③-列出某个目录下的所有子目录和文件"><a href="#③-列出某个目录下的所有子目录和文件" class="headerlink" title="③ 列出某个目录下的所有子目录和文件"></a>③ 列出某个目录下的所有子目录和文件</h5><p>一个栗子：</p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">public</span> <span class="keyword">static</span> List&lt;String&gt; <span class="title function_">listAllFile</span><span class="params">(File file)</span> &#123;</span><br><span class="line">    List&lt;String&gt; allFileList = <span class="keyword">new</span> <span class="title class_">ArrayList</span>&lt;&gt;();</span><br><span class="line">    <span class="keyword">if</span>(file.isFile()) &#123;</span><br><span class="line">        allFileList.add(file.getParent() + <span class="string">&quot;[&quot;</span> + file.getName() + <span class="string">&quot;]&quot;</span>);</span><br><span class="line">    &#125;<span class="keyword">else</span> &#123;</span><br><span class="line">        File[] childFiles = file.listFiles();</span><br><span class="line">        <span class="keyword">for</span> (File childFile : childFiles) &#123;</span><br><span class="line">            List&lt;String&gt; childFileList = listAllFile(childFile);</span><br><span class="line">            allFileList.addAll(childFileList);</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">return</span> allFileList;</span><br><span class="line">&#125;</span><br><span class="line"></span><br></pre></td></tr></table></figure>
<h5 id="④-汉诺塔问题"><a href="#④-汉诺塔问题" class="headerlink" title="④ 汉诺塔问题"></a>④ 汉诺塔问题</h5><blockquote>
<p>有n个大小不等的盘子放在一个塔A上面，自底向上按照从小到大的顺序排列。要求将所有n个盘子搬到另一个塔C上面，可以借助一个塔B中转，但是要满足任何时刻大盘子不能放在小盘子上面。</p>
</blockquote>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">public</span> <span class="keyword">static</span> <span class="type">int</span> <span class="title function_">hanNuoTa</span><span class="params">(<span class="type">char</span> a, <span class="type">char</span> b, <span class="type">char</span> c, <span class="type">int</span> n)</span> &#123;</span><br><span class="line">    <span class="type">int</span> <span class="variable">result</span> <span class="operator">=</span> <span class="number">0</span>;</span><br><span class="line">    <span class="keyword">if</span>(n == <span class="number">0</span>) &#123;</span><br><span class="line">        <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="type">int</span> <span class="variable">n1</span> <span class="operator">=</span> hanNuoTa(a, c, b, n - <span class="number">1</span>);</span><br><span class="line">    move(a, c);</span><br><span class="line">    result++;</span><br><span class="line">    <span class="type">int</span> <span class="variable">n2</span> <span class="operator">=</span> hanNuoTa(b, a, c, n - <span class="number">1</span>);</span><br><span class="line">    <span class="keyword">return</span> n1 + result + n2;</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title function_">move</span><span class="params">(<span class="type">char</span> a, <span class="type">char</span> b)</span> &#123;</span><br><span class="line">    System.out.println(<span class="string">&quot;从&quot;</span> + a + <span class="string">&quot;移动到&quot;</span> + b);</span><br><span class="line">&#125;</span><br><span class="line"></span><br></pre></td></tr></table></figure>
<h4 id="递归算法转换成非递归算法"><a href="#递归算法转换成非递归算法" class="headerlink" title="递归算法转换成非递归算法"></a>递归算法转换成非递归算法</h4><blockquote>
<p> 递归算法实际上是一种分而治之的方法，它把复杂问题分解为简单问题来求解。对于某些复杂问题(例如hanio塔问题)，递归算法是一种自然且合乎逻辑的解决问题的方式，但是递归算法的执行效率通常比较差。因此，在求解某些问题时，常采用递归算法来分析问题，用非递归算法来求解问题；另外，有些程序设计语言不支持递归，这就需要把递归算法转换为非递归算法。将递归算法转换为非递归算法有两种方法，一种是直接求值，不需要回溯；另一种是不能直接求值，需要回溯。前者使用一些变量保存中间结果，称为直接转换法；后者使用栈保存中间结果，称为间接转换法</p>
</blockquote>

    </div>

    
    
    
        

  <div class="followme">
    <p>欢迎关注我的其它发布渠道</p>

    <div class="social-list">

        <div class="social-item">
          <a target="_blank" class="social-link" href="/atom.xml">
            <span class="icon">
              <i class="fa fa-rss"></i>
            </span>

            <span class="label">RSS</span>
          </a>
        </div>
    </div>
  </div>


      <footer class="post-footer">
          <div class="post-tags">
              <a href="/tags/java/" rel="tag"># java</a>
              <a href="/tags/%E7%AE%97%E6%B3%95/" rel="tag"># 算法</a>
          </div>

        


        
    <div class="post-nav">
      <div class="post-nav-item">
    <a href="/2020/08/16/mac%E6%89%B9%E9%87%8F%E4%BF%AE%E6%94%B9%E6%96%87%E4%BB%B6%E5%90%8D%E7%A7%B0/" rel="prev" title="mac批量修改文件名称">
      <i class="fa fa-chevron-left"></i> mac批量修改文件名称
    </a></div>
      <div class="post-nav-item">
    <a href="/2020/08/18/java%E5%BF%AB%E6%85%A2%E6%8C%87%E9%92%88/" rel="next" title="java快慢指针">
      java快慢指针 <i class="fa fa-chevron-right"></i>
    </a></div>
    </div>
      </footer>
    
  </article>
  
  
  



          </div>
          

<script>
  window.addEventListener('tabs:register', () => {
    let { activeClass } = CONFIG.comments;
    if (CONFIG.comments.storage) {
      activeClass = localStorage.getItem('comments_active') || activeClass;
    }
    if (activeClass) {
      let activeTab = document.querySelector(`a[href="#comment-${activeClass}"]`);
      if (activeTab) {
        activeTab.click();
      }
    }
  });
  if (CONFIG.comments.storage) {
    window.addEventListener('tabs:click', event => {
      if (!event.target.matches('.tabs-comment .tab-content .tab-pane')) return;
      let commentClass = event.target.classList[1];
      localStorage.setItem('comments_active', commentClass);
    });
  }
</script>

        </div>
          
  
  <div class="toggle sidebar-toggle">
    <span class="toggle-line toggle-line-first"></span>
    <span class="toggle-line toggle-line-middle"></span>
    <span class="toggle-line toggle-line-last"></span>
  </div>

  <aside class="sidebar">
    <div class="sidebar-inner">

      <ul class="sidebar-nav motion-element">
        <li class="sidebar-nav-toc">
          文章目录
        </li>
        <li class="sidebar-nav-overview">
          站点概览
        </li>
      </ul>

      <!--noindex-->
      <div class="post-toc-wrap sidebar-panel">
          <div class="post-toc motion-element"><ol class="nav"><li class="nav-item nav-level-4"><a class="nav-link" href="#%E5%9F%BA%E6%9C%AC%E6%A6%82%E5%BF%B5"><span class="nav-number">1.</span> <span class="nav-text">基本概念</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%80%92%E5%BD%92%E7%AE%97%E6%B3%95%E8%A7%A3%E5%86%B3%E9%97%AE%E9%A2%98%E7%9A%84%E7%89%B9%E7%82%B9%EF%BC%9A"><span class="nav-number">1.1.</span> <span class="nav-text">递归算法解决问题的特点：</span></a></li></ol></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E5%87%A0%E4%B8%AA%E6%A0%97%E5%AD%90"><span class="nav-number">2.</span> <span class="nav-text">几个栗子</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E2%91%A0-%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E6%95%B0%E5%88%97"><span class="nav-number">2.1.</span> <span class="nav-text">① 斐波那契数列</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E2%91%A1-n-%E7%9A%84%E9%98%B6%E4%B9%98"><span class="nav-number">2.2.</span> <span class="nav-text">② n 的阶乘</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E2%91%A2-%E5%88%97%E5%87%BA%E6%9F%90%E4%B8%AA%E7%9B%AE%E5%BD%95%E4%B8%8B%E7%9A%84%E6%89%80%E6%9C%89%E5%AD%90%E7%9B%AE%E5%BD%95%E5%92%8C%E6%96%87%E4%BB%B6"><span class="nav-number">2.3.</span> <span class="nav-text">③ 列出某个目录下的所有子目录和文件</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E2%91%A3-%E6%B1%89%E8%AF%BA%E5%A1%94%E9%97%AE%E9%A2%98"><span class="nav-number">2.4.</span> <span class="nav-text">④ 汉诺塔问题</span></a></li></ol></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E9%80%92%E5%BD%92%E7%AE%97%E6%B3%95%E8%BD%AC%E6%8D%A2%E6%88%90%E9%9D%9E%E9%80%92%E5%BD%92%E7%AE%97%E6%B3%95"><span class="nav-number">3.</span> <span class="nav-text">递归算法转换成非递归算法</span></a></li></ol></div>
      </div>
      <!--/noindex-->

      <div class="site-overview-wrap sidebar-panel">
        <div class="site-author motion-element" itemprop="author" itemscope itemtype="http://schema.org/Person">
  <p class="site-author-name" itemprop="name">田园隐士</p>
  <div class="site-description" itemprop="description">talk is cheap, show me the code</div>
</div>
<div class="site-state-wrap motion-element">
  <nav class="site-state">
      <div class="site-state-item site-state-posts">
          <a href="/archives/">
        
          <span class="site-state-item-count">347</span>
          <span class="site-state-item-name">日志</span>
        </a>
      </div>
      <div class="site-state-item site-state-categories">
            <a href="/categories/">
        <span class="site-state-item-count">53</span>
        <span class="site-state-item-name">分类</span></a>
      </div>
      <div class="site-state-item site-state-tags">
            <a href="/tags/">
        <span class="site-state-item-count">115</span>
        <span class="site-state-item-name">标签</span></a>
      </div>
  </nav>
</div>



      </div>

    </div>
  </aside>
  <div id="sidebar-dimmer"></div>


      </div>
    </main>

    <footer class="footer">
      <div class="footer-inner">
        

        

<div class="copyright">
  
  &copy; 
  <span itemprop="copyrightYear">2022</span>
  <span class="with-love">
    <i class="fa fa-heart"></i>
  </span>
  <span class="author" itemprop="copyrightHolder">田园隐士</span>
    <span class="post-meta-divider">|</span>
    <span class="post-meta-item-icon">
      <i class="fa fa-chart-area"></i>
    </span>
    <span title="站点总字数">587k</span>
    <span class="post-meta-divider">|</span>
    <span class="post-meta-item-icon">
      <i class="fa fa-coffee"></i>
    </span>
    <span title="站点阅读时长">8:53</span>
</div>
  <div class="powered-by">由 <a href="https://hexo.io/" class="theme-link" rel="noopener" target="_blank">Hexo</a> & <a href="https://muse.theme-next.org/" class="theme-link" rel="noopener" target="_blank">NexT.Muse</a> 强力驱动
  </div>

        
<div class="busuanzi-count">
  <script async src="https://busuanzi.ibruce.info/busuanzi/2.3/busuanzi.pure.mini.js"></script>
    <span class="post-meta-item" id="busuanzi_container_site_uv" style="display: none;">
      <span class="post-meta-item-icon">
        <i class="fa fa-user"></i>
      </span>
      <span class="site-uv" title="总访客量">
        <span id="busuanzi_value_site_uv"></span>
      </span>
    </span>
    <span class="post-meta-divider">|</span>
    <span class="post-meta-item" id="busuanzi_container_site_pv" style="display: none;">
      <span class="post-meta-item-icon">
        <i class="fa fa-eye"></i>
      </span>
      <span class="site-pv" title="总访问量">
        <span id="busuanzi_value_site_pv"></span>
      </span>
    </span>
</div>








      </div>
    </footer>
  </div>

  
  <script src="/lib/anime.min.js"></script>
  <script src="/lib/velocity/velocity.min.js"></script>
  <script src="/lib/velocity/velocity.ui.min.js"></script>

<script src="/js/utils.js"></script>

<script src="/js/motion.js"></script>


<script src="/js/schemes/muse.js"></script>


<script src="/js/next-boot.js"></script>




  




  
<script src="/js/local-search.js"></script>













  

  

  

</body>
</html>
